Method for generating a cross-media aircraft water-impact trajectory based on a proxy model prediction

Abstract

The application discloses a method for generating a water-impact trajectory of a trans-medium aircraft based on a proxy model prediction, and belongs to the field of aircraft trajectory planning.The application models a trajectory generation problem of the trans-medium aircraft as a nonlinear programming problem with constraint conditions, solves the problem based on a pseudo-spectrum method, and obtains a feasible flight trajectory in an air segment that satisfies the constraint conditions, thereby improving the reliability of the trajectory generation of the trans-medium aircraft.The application uses a Latin hypercube design as a sampling method, can accurately reconstruct an input distribution through a limited number of iterations of sampling comparison, provides samples with higher spatial coverage for construction of the proxy model, reduces modeling errors caused by the use of a simplified model by the trans-medium aircraft, and has higher accuracy of a prediction result of a state quantity of the aircraft after the water-impact segment.The application performs nonlinear mapping on the state quantity before and after the water-impact segment through a proxy model constructed by a finite element software simulation, does not need to derive an accurate water-impact segment dynamic equation, and significantly reduces the calculation complexity caused by modeling.

Description

TECHNICAL FIELD

[0001] The application relates to a cross-medium aircraft water-impact trajectory generation method based on agent model prediction and belongs to the technical field of aircraft trajectory planning. BACKGROUND

[0002] The cross-medium aircraft is a special aircraft with air-sea dual-purpose operation capability, which not only has the characteristics of an aircraft and an underwater vehicle, but also can break through the medium isolation of water and air space, improve the reliability of cross-water and air task success, and has great application potential. Cross-medium aircraft trajectory planning is one of the key technologies to realize autonomous flight. Near-surface sliding jump, as a special flight mode of the cross-medium aircraft, has better maneuverability and accuracy than high-altitude projection, which can effectively improve the flight range and survival ability of the aircraft.

[0003] The cross-medium aircraft task trajectory generation needs to be designed considering the characteristics of different flight stages. The entire flight stage can be divided into an air flight section and a water impact section. The trajectory generation of the air flight section needs to consider the flight performance, state boundary and other constraints of the cross-medium aircraft, and takes the shortest time or the shortest flight range as the performance index to generate a feasible optimal trajectory for the aircraft. For the water impact section, the existing cross-medium aircraft water impact trajectory generation method mainly considers the interaction force between the fluid and the aircraft, accurately models the cross-medium aircraft, and solves the corresponding results, or abstracts the aircraft as a flat plate or a cylinder for dynamic modeling. However, since the water impact process includes the interaction process among air, water and aircraft, the motion of the cross-medium aircraft has randomness and unknownness, and the related force is difficult to obtain an explicit expression. At the same time, there are many types of cross-medium aircrafts, and their shapes are different, so the simulation model is difficult to calculate and takes a long time. Therefore, it is necessary to carry out the integration research of the cross-medium aircraft and the agent model, which can reduce the model research cost under the premise of meeting the reliability.

[0004] In view of the above problems, the application provides a cross-medium aircraft water-impact trajectory generation method based on an agent model, which is used for planning the water-impact flight trajectory of the cross-medium aircraft in the whole process. The agent model is constructed by simulating and collecting state quantity samples of the cross-medium aircraft before and after water impact under different working conditions, and the nonlinear mapping of the state quantities before and after water impact is carried out, so as to predict the state after water impact in the real situation, solve the problems of difficult derivation of the accurate dynamic model of the cross-medium aircraft in the water impact section and low accuracy of the simplified modeling, and provide reliable technical support for the completion of the multi-stage flight task of the cross-medium aircraft. SUMMARY

[0005] To address the challenges of deriving accurate dynamic models for the water-impact phase of cross-medium aircraft and the low accuracy of simplified modeling, this invention provides a method for generating the water-impact bounce trajectory of cross-medium aircraft based on surrogate model prediction. This method involves simulating and sampling different operating conditions during the water-impact phase, constructing a surrogate model to nonlinearly map the state variables before and after water impact, and then modeling the cross-medium aircraft trajectory generation problem as an optimal control problem. The pseudospectral method is then used to iteratively solve the nonlinear optimal control problem until all trajectory constraints are satisfied, generating the flight trajectory of the cross-medium aircraft throughout the entire water-impact process. This invention can predict the aircraft's state after water impact, avoiding the computational difficulties and time-consuming nature of real aircraft simulation models, and offers advantages of high accuracy and high reliability.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] A method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction, characterized by the following steps:

[0008] Step 1: Generate a set of Latin hypersquare sampling points, with the four dimensions being velocity and tilt angle θ. sample Speed ​​V sample Angle of attack α sample With mass m sample The response values ​​corresponding to the Latin hypersquare sampling point set were obtained through finite element software simulation, i.e., the positions of the transmedium spacecraft before and after water impact [x]. res ,y res Speed ​​V res Pitch angle Angle of attack α res A database of sample points is constructed from several sets of response values.

[0009] Step 2: Construct a radial basis function (RBF) surrogate model using the sample point database from Step 1;

[0010]

[0011] In the formula,

[0012]

[0013] Where z is the input value, n s To determine the sample size for constructing the radial basis function surrogate model, The weighting coefficients are calculated using equations (2) to (3). φ is the radial function; c i Let w represent the set of sample points constructed in step one, and w represent the response value of the sample points in step one. The output value of the proxy model is the flight state of the cross-medium aircraft after it strikes the water;

[0014] Step three: setting initial simulation parameters of the trans-medium aircraft; the initial simulation parameters include: trans-medium aircraft thrust P(t), flight time t i (i = phase1, phase2, phase3), initial position [x0, y0], initial velocity V0, initial mass m0, initial ballistic angle θ0, initial angle of attack α0, state boundary s min ,s max , control boundary u min ,u max , and maximum allowable error ε d ;

[0015] Step four: based on the performance index, dynamic constraint, state constraint and control quantity constraint, establishing an optimal control model of the trans-medium aircraft for the air gliding segment and the low-altitude flying segment;

[0016] The performance index J of the trans-medium aircraft trajectory generation is the maximum flight range:

[0017] J = -x (4)

[0018] x is the horizontal position of the trans-medium aircraft;

[0019] The dynamic constraint of the trans-medium aircraft is expressed as:

[0020]

[0021] Wherein, s = [V, θ, x, y, m, α] is the state quantity of the trans-medium aircraft, V is the speed, θ is the ballistic angle, x is the horizontal position, y is the vertical position, m is the mass, and α is the angle of attack; P represents the aircraft thrust, X represents the aerodynamic drag, Y represents the aerodynamic lift, m c represents the mass flow rate, is the angle of attack change rate; g is the gravitational acceleration;

[0022] The state constraints of the high-altitude flying segment, the low-altitude flying segment and the post-impact segment of the trans-medium aircraft include: the initial state constraint as formula (6), the terminal state constraint as formula (7) and the state boundary constraint as formula (8);

[0023]

[0024] θ(t f ) = θ f y(t f ) = y f (7)

[0025]

[0026] Wherein, t0 represents the initial time, t fdenotes the terminal time, V(t) denotes the value of V at time t, and the remaining variables are defined similarly; s0= [V0, θ0, x0, y0, m0, α0] denotes the initial state of each phase, [θ f ,y f ] denotes the terminal state of each phase, s min = [V min ,θ min ,x min ,y min ,m min ,α min ] and s max = [V max ,θ max ,x max ,y max ,m max ,α max ] respectively denote the lower and upper bounds of the state of each phase;

[0027] In order to avoid instability of the control system due to high-frequency changes in the control variable, the range of change of the control variable needs to be limited, i.e.

[0028]

[0029] wherein the control variable is the change rate of the attack angle, denotes the minimum value of the change rate of the attack angle, denotes the maximum value of the change rate of the attack angle; s and s

[0030] denote the upper and lower bounds of the control variable of each phase, respectively; An optimal control problem model for trajectory generation in the air phase of a trans-medium aircraft is established according to equations (4)-(9)

[0031]

[0032] wherein u is the control variable, i.e. is the change rate of the attack angle of the i-th phase; x i is the horizontal position of the aircraft of the i-th phase; phase1 denotes the high-altitude flight phase, phase2 denotes the low-altitude flight phase, and phase3 denotes the post-impact phase, all of which are the air flight phases of the trans-medium aircraft; the problem needs to find a set of control variables to minimize the performance index under the condition that each phase satisfies the constraints;

[0033] Step five: the optimal control problem established in step four is discretized and numerically approximated to convert it into a nonlinear programming problem;

[0034] Step 5.1: the discretization process is as follows:

[0035] the interval [t0, tf The time interval is uniformly divided into K grid sub-intervals, and the time step of each grid sub-interval is Δt = (t... f -t0) / K, then for each grid subinterval [t k-1 ,t k The state and control variables on the equation are discretized at discrete points and approximated by constructing interpolation polynomials, thereby transforming the differential equation into an algebraic equation constraint.

[0036] For each grid subinterval, the time domain t∈[t k-1 ,t k Transform the variable τ∈[-1,1] using equation (11);

[0037]

[0038] Let the state variables and control variables of the k-th grid sub-interval be s, respectively. (k) (τ) and u (k) (τ), to ensure the continuity of the state between each grid sub-interval, the inner grid point constraint condition shown in equation (12) is added, that is

[0039] s (k) (+1)=s (k+1) (-1), k=0,1,...,K-1 (12)

[0040] By transforming equations (11) and (12), the optimal control problem can be transformed. The problem is transformed into a multi-interval optimal control problem. The performance index shown in equation (4) is transformed into minimizing a multi-interval Bolza-type cost function:

[0041]

[0042] Where Φ represents the Mayer-type cost function and G represents the Lagrange-type cost function.

[0043] In summary, through the transformations of equations (11) to (13), the optimal control problem of multi-interval Bolza-type performance indices considering the addition of internal network point constraints is solved. It is expressed as follows:

[0044]

[0045] Where f and These are dynamic constraints and state quantity start-end constraints, respectively.

[0046] Step 5.2: Approximate the dynamic equations, boundary conditions, and process constraints of the transmedium vehicle using numerical approximation, transforming them into the general solution form of the pseudospectral method, thereby converting the equations established in Step 5.1 into a more comprehensive solution. This is transformed into a nonlinear programming problem.

[0047] Let s (k) (τ) and u (k) (τ) denote the state and control in the kth sub-interval [t k-1 , t k ] respectively.

[0048] Take N k + 1 LGR points and the end point as nodes, in the interval τ∈[-1,1], N k + 1 Lagrange interpolation polynomials are used to approximate the state s (k) (τ) and control u (k) (τ) :

[0049]

[0050] where S (k) (τ) and U (k) (τ) are the approximated state and control, S i (k) denotes the value of the state at the ith collocation point in the interval [t k-1 , t k ], and U i (k) denotes the value of the control at the ith collocation point in the interval [t k-1 , t k ]; L i (τ)i=1,...,N k + 1 are N k + 1 Lagrange interpolation polynomials, i.e.,

[0051]

[0052] where τ i and τ j are any two distinct collocation points in the interval [t k-1 , t k ].

[0053] Differentiating equation (15), we have

[0054]

[0055] Then the dynamics differential equation constraints at the LGR points are converted into algebraic equation constraints:

[0056]

[0057] where is the pseudo-spectral differential matrix of the kth sub-interval.

[0058] The boundary constraint on each grid sub-interval N k is:

[0059]

[0060] The state constraint on each grid point is:

[0061]

[0062] The integral term in the multi-interval Bolza performance index (13) is approximated by the multi-interval Gauss integral to obtain

[0063]

[0064] wherein, is the Lagrange-type cost function in the kth sub-interval; is the Legendre-Gauss-Radau weight in the kth sub-interval, expressed as:

[0065]

[0066] Through the numerical approximation process of equations (15)-(22), the following equation is finally obtained: which is a nonlinear programming problem with constraints

[0067]

[0068] Step six: solve using the pseudospectral method to obtain the solution of , i.e., the flight trajectory of the hypersonic vehicle in the high-altitude flight segment and the low-altitude flight segment;

[0069] Step seven: according to equation (25), if the step six result satisfies equation (25), output the solution of , and execute step eight; if not, increase the discrete points through equation (26), and go to step five;

[0070]

[0071] wherein, is the s th sampling point selected in the k th sub-interval [t k-1 , t k ], ceil(·) is the ceiling function, N d is a positive integer used to adjust the number of newly added discrete nodes; represents the maximum error in the k th sub-interval;

[0072] Step eight: output​ The solving result is obtained, and the flight trajectory of the high-altitude flight segment and the low-altitude flight segment is obtained, and the flight state after the trans-medium aircraft hits the water is obtained through the proxy model constructed in step two;

[0073] The velocity inclination angle θ f , the velocity V f , the attack angle α f , and the mass m f in the trajectory final state of the solving result are input into the proxy model (1) as independent variables, and the initial state of the trans-medium aircraft after hitting the water is obtained, that is:

[0074] x input =[θ f ,V f ,α f ,m f ] (27)

[0075]

[0076] Wherein, x input represents the final state of the trajectory, x output represents the aircraft state quantity obtained by solving, and is also represented as the initial state x 0,phase3 of the post-hitting water segment;

[0077] Step nine: based on the initial state x 0,phase3 of the post-hitting water segment obtained in step eight, the optimal control model of the post-hitting water segment is established, and step five is converted to solve the flight trajectory of the post-hitting water segment;

[0078] Step ten: output and splice the high-altitude flight segment trajectory obtained in step six, the low-altitude flight segment trajectory and the post-hitting water segment flight trajectory obtained in step nine, to obtain all the trajectories, that is, the trans-medium aircraft hitting water trajectory generation result based on the proxy model prediction;

[0079] Further comprising step eleven: according to the aircraft hitting water trajectory generation result obtained in step ten, the complete flight trajectory of the trans-medium aircraft in the multi-task stage can be obtained, so that the trans-medium aircraft reaches the target position range through one or more hitting water bounces from a given position under the premise of meeting the constraints of each stage, and the trans-medium aircraft hitting water flight with high precision and low calculation amount is realized.

[0080] Beneficial effects:

[0081] 1. The trans-medium aircraft hitting water trajectory generation method based on the proxy model prediction disclosed in the application models the trans-medium aircraft trajectory generation problem as a nonlinear programming problem with constraints, and solves the problem based on the pseudospectral method, so that the feasible flight trajectory in the air segment meeting the constraints is obtained, and the reliability of the trans-medium aircraft trajectory generation is improved.

[0082] 2. The cross-medium aircraft water-impact bounce trajectory generation method based on the agent model prediction disclosed in the application uses Latin hypercube design as a sampling method, can accurately reconstruct the input distribution through a limited number of sampling iterations, provides samples with higher spatial coverage for the construction of the agent model, reduces the modeling error caused by the use of a simplified model by the cross-medium aircraft, and has higher accuracy of the prediction result of the state quantity of the aircraft after the water-impact section.

[0083] 3. The cross-medium aircraft water-impact bounce trajectory generation method based on the agent model prediction disclosed in the application performs nonlinear mapping on the state quantity before and after the water-impact section through the agent model constructed by the finite element software simulation, does not need to derive the accurate water-impact section dynamics equation, significantly reduces the calculation complexity caused by modeling, and improves the efficiency of the cross-medium aircraft water-impact bounce trajectory generation. BRIEF DESCRIPTION OF DRAWINGS

[0084] Figure 1 The flowchart of the aircraft water-impact bounce flight trajectory generation method based on the agent model prediction of the application;

[0085] Figure 2 The cross-medium aircraft flight trajectory obtained by the method of the application in the specific implementation example;

[0086] Figure 3 The local enlarged view of the water-impact section of the cross-medium aircraft obtained by the method of the application in the specific implementation example;

[0087] Figure 4 The speed curve of the cross-medium aircraft obtained by the method of the application in the specific implementation example;

[0088] Figure 5 The change curve of the attitude angle in the result obtained by the method of the application in the specific implementation example;

[0089] Figure 6 The curve of the change rate of the attack angle in the result obtained by the method of the application in the specific implementation example. DETAILED DESCRIPTION

[0090] In order to better illustrate the purposes and advantages of the application, the application is further described below through the cross-medium aircraft water-impact bounce trajectory generation example, combined with the drawings and tables, and the comprehensive performance of the application is verified and analyzed.

[0091] Known conditions: The cross-medium aircraft starts flying from a high altitude y0=150 m, flies through a high-altitude section for t1=20 s and a low-altitude section for t2=20 s, starts water contact after the water-impact, leaves the water surface after one water-impact bounce, flies for t3=10 s after the water-impact, reaches the specified position range, and ends the task.

[0092] AsFigure 1 As shown in the figure, the specific implementation steps of the method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction disclosed in this embodiment are as follows:

[0093] Step 1: Randomly generate a set of Latin hypersquare sampling points and obtain their response values.

[0094] A set of Latin hypersquare sampling points is generated, X = lhsdesign(50,4), and the velocity tilt angle θ of the Latin hypersquare sampling point set is obtained by simulation using ANSYS software. sample Speed ​​V sample Angle of attack α sample Mass m sample Position of the transmedium-mounted vehicle before and after water impact [x] res ,y res Speed ​​V res Pitch angle θ res Angle of attack α res Response values, etc.

[0095] Step 2: Construct an RBF surrogate model using the state variables before and after water impact from the sample point database.

[0096]

[0097] Among them, the weighting coefficient It can be obtained by solving the following formula.

[0098]

[0099] In this example, n s The sample size for constructing the RBF surrogate model is set to 4; φ(||||) is a quadratic function, i.e., φ(r) = (r| ... 2 +1) 1 / 2

[0100] Step 3: Input the initial state, mission parameters, state constraints, and algorithm parameter settings of the cross-medium spacecraft.

[0101] In this example, the initial thrust of the transmedium vehicle is set to P0 = 361.3 N, and the initial mass flow rate is... The initial time is t0 = 0s, the high-altitude flight time is t1 = 20s, the low-altitude flight time is t2 = 20s, and the flight time after hitting the water is t3 = 10s.

[0102] The initial position of the transmedium vehicle is [x0, y0] = [0km, 150m]. T Initial velocity V0 = 500 m / s, initial trajectory inclination angle θ0 = 0°, initial mass m0 = 280 kg, initial angle of attack α0 = 0°.

[0103] The boundary constraint values of the state variables and control variables in the high-altitude flight segment are shown in equation (31):

[0104]

[0105] The boundary constraint values of the state variables and control variables in the low-altitude flight segment are shown in equation (32):

[0106]

[0107] The boundary constraint values of the state variables and control variables in the post-impact segment are shown in equation (33):

[0108]

[0109] Step four: For the trajectory generation problem of the cross-medium aircraft in the air gliding segment and the low-altitude flight segment, an optimal control problem is established for the performance index, dynamic constraints, state constraints, and control variable constraints, as shown in equation (34).

[0110]

[0111] where, represents the derivative of the state variable s with respect to time t, f(s, t) represents the dynamic differential equation, s(t i,0 ) represents the value of the state variable at the initial time of the i-th segment, s(t i,f ) represents the value of the state variable at the terminal time of the i-th segment, s i,min represents the minimum value of the state variable in the i-th segment, s i,max represents the maximum value of the state variable in the i-th segment.

[0112] Step five: The optimal control problem established in step four is discretized and numerically approximated to convert it into a nonlinear programming problem.

[0113] Step 5.1: Discretization, converting the continuous problem into a discrete problem.

[0114] Select the discrete interval number K = 100, and divide the interval [t0, t f ] into 100 grid subintervals, with a time step of △t = (t f -t0) / 100. Then, discretize the state variables and control variables at the discrete points in each subinterval [t k-1 , t k ].

[0115] In summary, the optimal control problem of the multi-interval Bolza type performance index with increased inner grid point constraints is represented as follows:

[0116] ​

[0117] where f and are the dynamic and state quantity end constraints, respectively.

[0118] Step 5.2: Convert the discrete problem into the general solution form of the pseudospectral method.

[0119] Numerically approximate equation (35) to establish a nonlinear programming problem with constraints

[0120]

[0121] Step six: solve using the pseudospectral method to obtain the solution of , i.e., the flight trajectory of the trans-medium aircraft in the high-altitude flight segment and the low-altitude flight segment;

[0122] Step seven: determine whether the approximation error of the step six result is less than the allowable error. If it is, output the solution trajectory and perform step eight; if it is not, increase the discrete points and go to step four.

[0123] The convergence condition is shown in equation (37), and the discrete point increase method is shown in equation (38).

[0124]

[0125] where is the s-th sampling point selected in the k-th sub-interval [t k-1 , t k ], ceil(·) is the ceiling function, N k is the current number of discrete points, N k,new is the adjusted number of discrete points, and N d is a positive integer used to adjust the number of newly added discrete nodes.

[0126] Step eight: output the air segment trajectory of step six, and obtain the flight state of the trans-medium aircraft after hitting the water through the surrogate model.

[0127] Take the velocity inclination θ f , velocity V f , attack angle α f , and mass m f in the final state of the trajectory solved in step six as the independent variables input into the surrogate model (1) to obtain the initial state of the trans-medium aircraft after hitting the water, i.e.,

[0128] x input = [θ f , V f , α f , m f ] (39)

[0129]

[0130] where x input represents the solved trajectory final state, x output represents the solved aircraft state quantity after water impact, and also represents the initial state x 0,phase3 of the post-water impact air trajectory.

[0131] Step nine: based on the solved post-water impact initial state in step eight, an optimal control model of the post-water impact section is established, and step five is turned to obtain the post-water impact air flight trajectory of the trans-medium aircraft.

[0132] Step ten: the high-altitude flight section trajectory obtained in step six, the low-altitude flight section trajectory, and the post-water impact flight trajectory obtained in step nine are output and spliced to obtain all trajectories, i.e. the aircraft water impact bounce flight trajectory generation result based on the proxy model prediction.

[0133] Step eleven: according to the aircraft water impact bounce flight trajectory generation result obtained in step ten, the trans-medium aircraft is made to reach the target position range from a given position through one or more water impact bounces under the premise of meeting the constraints of each stage, so as to realize the trans-medium aircraft water impact flight with high precision and low calculation amount.

[0134] For the above specific example, the trajectory result obtained by the aircraft water impact bounce trajectory generation method based on the proxy model prediction of the present application is as shown in Figure 2 . Figure 2 In the figure, the blue diamond line type is the trajectory of the high-altitude section of the aircraft, the green circle line type is the flight trajectory of the low-altitude section of the aircraft, and the red square line type is the flight trajectory of the post-water impact section of the aircraft. Figure 2 A local enlarged view of the water impact section is given, and it can be seen from Figure 2 and Figure 3 that the trajectory generated by the method proposed in the present application can guide the trans-medium aircraft to fly to the target position through one water impact bounce from the target position. Figure 4 The velocity curve corresponding to the solving result is given, which satisfies the upper and lower bound constraints of the velocity of each section. Figure 5 The attitude angle change curve of the trans-medium aircraft is given, and it can be seen that the trans-medium aircraft satisfies the upper and lower bound constraints of the attitude angle of each section. Figure 6 The angle of attack change rate is given, and it can be seen that the control quantity of the trans-medium aircraft is always within the interval [-2° / s, 2° / s], satisfying the control quantity constraint.

[0135] According to the simulation results and analysis of the cross-medium aircraft water-impact bounce trajectory generation example described above, the cross-medium aircraft water-impact bounce trajectory generation method based on proxy model prediction can make the cross-medium aircraft successfully touch the water after flying in the air at a height y0=150 m for a high-altitude section of t1=20 s and a low-altitude section of t2=20 s, leave the water surface after one water-impact bounce, and reach the specified position range after flying for t3=10 s after water-impact, thereby ending the task. The entire process meets the state constraints and control constraints of each stage, safely completes the entire process of flight, and achieves the task requirements. Therefore, the present application has strong engineering practicability and basically achieves the intended purpose of the invention.

[0136] The specific description described above further details the purpose, technical solutions and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not intended to limit the protection scope of the application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the application should be included in the protection scope of the application.

Claims

1. A method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction, characterized in that: Includes the following steps: Step 1: Generate a set of Latin hypersquare sampling points, with the four dimensions being velocity and tilt angle θ. sample Speed ​​V sample Angle of attack α sample With mass m sample The response values ​​corresponding to the Latin hypersquare sampling point set were obtained through finite element software simulation, i.e., the positions of the transmedium spacecraft before and after water impact [x]. res ,y res Speed ​​V res Pitch angle Angle of attack α res A database of sample points is constructed from several sets of response values. Step 2: Construct a radial basis function (RBF) surrogate model using the sample point database from Step 1; Where z is the input value, n s To determine the sample size for constructing the radial basis function surrogate model, Here, φ is the weighting coefficient, and c is the radial function; i This represents the sample points constructed in step one; The output value of the proxy model is the flight state of the cross-medium aircraft after it strikes the water; Step 3: Set the initial simulation parameters for the cross-medium aircraft; The initial simulation parameters include: the cross-medium spacecraft thrust P(t), and the flight time t at each stage. i (i = phase1, phase2, phase3), initial position [x0, y0], initial velocity V0, initial mass m0, initial trajectory inclination angle θ0, initial angle of attack α0, state boundary s min ,s max Control boundary u min ,u max and the maximum permissible error ε d ; Step 4: For the trajectory generation problem of the high-altitude and low-altitude flight segments of the cross-medium aircraft, establish an optimal control problem model with performance indicators, dynamic constraints, state constraints, and control quantity constraints; Step 5: The optimal control problem established in Step 4 is discretized and numerically approximated to transform it into a nonlinear programming problem; Step Six: For the constrained nonlinear programming problem established in Step Five, the pseudospectral method is used to solve it, and the trajectories of the high-altitude and low-altitude flight segments of the cross-medium aircraft are obtained. Step 7: Determine whether the approximate error of the flight trajectory result obtained in Step 6 is less than the allowable error; if it is satisfied, output the solved trajectory and proceed to Step 8; if it is not satisfied, add discrete points and go to Step 4. Step 8: Output the aerial trajectory obtained in Step 7, and obtain the flight state of the cross-medium aircraft after water impact through the surrogate model; Step 9: Based on the initial state after water impact obtained in Step 8, establish the optimal control model for the later stage of water impact, and solve it in Step 5 to obtain the flight trajectory for the later stage of water impact. Step 10: Output all the trajectories obtained by splicing together Step 6 and Step 9, which is the result of generating the water-bounce flight trajectory of the cross-medium aircraft based on the surrogate model prediction.

2. The method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction as described in claim 1, characterized in that: Step four is implemented as follows: The performance index J for cross-medium vehicle trajectory generation is the maximum flight range, as shown in equation (2): J = -x (2) x represents the horizontal position of the transmedium aircraft; The dynamic constraints of a transmedium-based aircraft are expressed by the following system of differential equations: Where s = [V,θ,x,y,m,α] represents the state variables of the transmedium vehicle, where V is velocity, θ is trajectory inclination angle, x is horizontal position, y is vertical position, m is mass, and α is angle of attack; P represents vehicle thrust, X represents aerodynamic drag, Y represents aerodynamic lift, and m... c Indicates mass flow rate, is the rate of change of angle of attack; g is the acceleration due to gravity; The state constraints of the high-altitude flight segment, low-altitude flight segment, and post-water impact segment of the cross-medium aircraft include: initial state constraints as shown in equation (4), terminal state constraints as shown in equation (5), and state boundary constraints as shown in equation (6). θ(t f )=θ f , y(t f )=y f (5) Where t0 represents the initial time, t f The terminal time is represented by V(t), which represents the value of V at time t, and the other variables follow the same logic; s0=[V0,θ0,x0,y0,m0,α0] represents the initial state of each stage, [θ f ,y f ] represents the final state of the state variables at each stage, s min =[V min ,θ min ,x min ,y min ,m min ,α min ] and s max =[V max ,θ max ,x max ,y max ,m max ,α max ] These represent the lower and upper boundaries of the state at each stage, respectively; Considering the capabilities of the actuator and to prevent the control system from becoming unstable due to high-frequency changes in the control quantity, it is necessary to limit the range of change of the control quantity, i.e. Among them, control quantity For the rate of change of angle of attack, This represents the minimum rate of change of angle of attack. This indicates the maximum rate of change of angle of attack; Based on the performance index given in equation (2) and the constraints given in equations (3) to (7), an optimal control model for the trajectory generation problem of a cross-medium aircraft in the air segment is established. Where u is the control variable, i.e. x is the rate of change of the angle of attack for the i-th segment; i Let be the horizontal position of the aircraft in the i-th segment; phase1 represents the high-altitude flight segment, phase2 represents the low-altitude flight segment, and phase3 represents the post-water impact segment, all of which are the aerial flight segments of the cross-medium aircraft; the problem requires finding a set of control variables that minimize the performance index under the condition that each segment satisfies the constraints.

3. The method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction as described in claim 2, characterized in that: Step five is implemented as follows: Step 5.1: The discretization process is as follows: The interval [t0, t] f The time interval is uniformly divided into K grid sub-intervals, and the time step of each grid sub-interval is Δt = (t... f -t0) / K, then for each grid subinterval [t k-1 ,t k The state and control variables on the equation are discretized at discrete points and approximated by constructing interpolation polynomials, thereby transforming the differential equation into an algebraic equation constraint. For each grid subinterval, the time domain t∈[t k-1 ,t k Transform the variable τ∈[-1,1] using equation (9); Let the state variables and control variables of the k-th grid sub-interval be s, respectively. (k) (τ) and u (k) (τ), to ensure the continuity of the state between each grid sub-interval, the inner grid point constraint condition shown in equation (10) is added, that is s (k) (+1)=s (k+1) (-1), k=0,1,...,K-1 (10) By transforming equations (9) and (10), the optimal control problem can be transformed. Transformed into a multi-interval optimal control problem, the performance index shown in equation (2) is transformed into minimizing a multi-interval Bolza-type cost function: Where Φ represents the Mayer-type cost function and G represents the Lagrange-type cost function; In summary, based on the transformations in equations (9) to (11), we consider the optimal control problem of multi-interval Bolza-type performance indices with added internal network point constraints. It is expressed as follows: Where f and These are dynamic constraints and state quantity start-end constraints, respectively. Step 5.2: Approximate the dynamic equations, boundary conditions, and process constraints of the transmedium vehicle using numerical approximation, transforming them into the general solution form of the pseudospectral method, thereby converting the equations established in Step 5.1 into a more comprehensive solution. This is transformed into a nonlinear programming problem. Let s (k) (τ) and u (k) (τ) represent the k-th subinterval [t] k-1 ,t k State and control variables within [the scope of the system]. Take N k LGR point and end point As a node, N is used in the interval τ∈[-1,1]. k +1 Lagrange interpolation polynomials for the state variable s (k) (τ) and control quantity u (k) (τ) is approximated as follows: Among them, S (k) (τ) and U (k) (τ) represent the approximate state and control variables, respectively, and S i (k) This indicates that the state quantity is in the interval [t]. k-1 ,t k The value of the i-th collocation point within ], U i (k) This indicates that the control quantity is in the interval [t]. k-1 ,t k The value of the i-th collocation point within L; i (τ)i=1,...,N k +1 represents N k The order Lagrange interpolation polynomial, i.e.: In the formula, τ i and τ j This indicates that the Radau pseudospectral method is effective in the interval [t]. k-1 ,t k Any two non-repeating collocations within [ ]; Differentiating equation (13), we get The dynamic differential equation constraints at the LGR point are then transformed into algebraic equation constraints: In the formula, Let be the pseudospectral differential matrix of the k-th subinterval; N within each grid sub-interval k The boundary constraints on each collocation point are: The state constraints on the network points are: The integral term in the multi-interval Bolza-type performance index (11) is approximated by the multi-interval Gaussian integral, yielding... In the formula, The Lagrange-type cost function is for the k-th subinterval; The Legendre-Gauss-Radau weights within the k-th subinterval are expressed as: Through the numerical approximation process of equations (13) to (20), the final result will be This is transformed into a nonlinear programming problem with constraints.

4. The method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction as described in claim 3, characterized in that: In step six, For the nonlinear programming problem shown in equation (22), the pseudospectral method is used to solve it and obtain the flight trajectories of the transmedium aircraft in the high-altitude and low-altitude segments.

5. The method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction as described in claim 4, characterized in that: In step seven, The convergence condition is shown in equation (23), and the discrete point addition method is shown in equation (24). in, For the k-th subinterval [t] k-1 ,t k The s-th sampling point is selected within ], ceil(·) is the floor function, and N d It is a positive integer used to adjust the number of newly added discrete nodes; It represents the maximum error within the k-th subinterval.

6. The method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction as described in claim 5, characterized in that: Step eight is implemented as follows: Solve for the velocity inclination angle θ in the final state of the trajectory in step six. f Speed ​​V f Angle of attack α f Mass m f As an independent variable, it is input into the surrogate model (1) to obtain the initial state of the transmedium aircraft after water impact, namely: x input =[θ f ,V f ,a f ,m f ] (25) Where, x input x represents the final state of the solved trajectory. output This represents the state variables of the aircraft after water impact, obtained from the solution, and also represents the initial state x in the post-water impact phase. 0,phase3。 7. The method for generating water-bounce trajectories of cross-medium aircraft based on surrogate model prediction as described in claims 1, 2, 3, 4, 5, or 6, characterized in that: It also includes step eleven: based on the water-bounce flight trajectory generation results of the cross-medium aircraft obtained in step ten, the complete flight trajectory of the cross-medium aircraft in the multi-mission stage can be obtained, so that the cross-medium aircraft can reach the target position range from a given position through one or more water-bounces under the premise of satisfying the constraints of each stage, thus realizing high-precision and low-computation cross-medium aircraft water-bounce flight.

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